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Kernel-based stochastic collocation for the random two-phase navier-stokes equations

: Griebel, Michael; Rieger, Christian; Zaspel, Peter


International journal for uncertainty quantification 9 (2019), Nr.5, S.471-492
ISSN: 2152-5080
ISSN: 2152-5099
Deutsche Forschungsgemeinschaft DFG
SFB 1060; 211504053
Fraunhofer SCAI ()

In this work, we apply stochastic collocation methods with radial kernel basis functions for an uncertainty quantification of the random incompressible two-phase Navier-Stokes equations. Our approach is nonintrusive and we use the existing fluid dynamics solver NaSt3DGPF to solve the incompressible two-phase Navier-Stokes equation for each given realization. We are able to empirically show that the resulting kernel-based stochastic collocation is highly competitive in this setting and even outperforms some other standard methods.